 I will be able to identify and graph quadratic functions. Algebra 2 Foundations, pg 204.

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Presentation transcript:

 I will be able to identify and graph quadratic functions. Algebra 2 Foundations, pg 204

In the Solve It, you used the parabolic shape of the horse’s jump. A parabola is the graph of a quadratic function, which you can write in the form f(x) = ax² + bx + c, where a ≠ 0.  I will be able to identify and graph quadratic functions. Focus Question What is the vertex form of a quadratic function?  The vertex form of a quadratic function is f(x) = a(x-h)² + k, where a ≠ 0. All quadratic functions are transformations of the parent function, f(x) = x². Use vertex form to identify the transformations and graph a quadratic function.

Algebra 2 Foundations, pg 204 The vertex form of a quadratic function is f(x) = a(x-h)² + k, where a ≠ 0. The axis of symmetry is a line that vertically divides the parabola into two mirror images. The vertex of the parabola is the intersection of the parabola and its axis of symmetry. The equation of the axis of symmetry is x = h and the vertex is (h, k).  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 204  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 205  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 205  I will be able to identify and graph quadratic functions. Let’s take them one at a time.

Algebra 2 Foundations, pg 205  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 205  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 205  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 205  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 205  I will be able to identify and graph quadratic functions. The graphs of y = ax² and y = -ax² are reflections of each other in the x-axis. Increasing |a| stretches the graph vertically. Decreasing |a| compresses the graph vertically.

Algebra 2 Foundations, pg 205  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 206  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 206  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 206  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 206  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 206  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 206  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 207  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 207  I will be able to identify and graph quadratic functions. You can use the vertex form of the quadratic function, f(x) = a(x-h)² + k, to transform the graph of the parent function f(x) = x².

Algebra 2 Foundations, pg 208  I will be able to identify and graph quadratic functions. You can use the vertex form of the quadratic function, to model a real-world situation.

Algebra 2 Foundations, pg 207  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 209  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 209  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 209  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 209  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 210  I will be able to identify and graph quadratic functions.

Algebra 2 Foundations, pg 210  I will be able to identify and graph quadratic functions.